Treatise on Natural Philosophy, Volume 1, Part 1At the University Press, 1879 - Mechanics, Analytic |
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Results 1-5 of 32
Page 4
... direction cosines of the osculating plane , and the tortuosity , of a curve not in one plane , in terms of Cartesian triple co - ordinates , let , as before , So be the angle between the tangents at two points at a distance ds from one ...
... direction cosines of the osculating plane , and the tortuosity , of a curve not in one plane , in terms of Cartesian triple co - ordinates , let , as before , So be the angle between the tangents at two points at a distance ds from one ...
Page 5
... directions indicated by the order of the letters . Draw OS perpendicular to their plane in the direction from 0 ... direction cosines of OL be a , b , c ; OL ' a ' , b ' , c ' ; 00 " " 1 , m , n ; OR OS 99 a , ẞ , y ; λ , μ , ν ...
... directions indicated by the order of the letters . Draw OS perpendicular to their plane in the direction from 0 ... direction cosines of OL be a , b , c ; OL ' a ' , b ' , c ' ; 00 " " 1 , m , n ; OR OS 99 a , ẞ , y ; λ , μ , ν ...
Page 6
... direction cosines of the normal , PC , drawn towards the centre of curvature , C ; and λ , μ , v those of the perpendicular to the osculating plane drawn in the direc- tion relatively to PT and PC , corresponding to that of OZ ...
... direction cosines of the normal , PC , drawn towards the centre of curvature , C ; and λ , μ , v those of the perpendicular to the osculating plane drawn in the direc- tion relatively to PT and PC , corresponding to that of OZ ...
Page 7
... direction cosines of the osculating plane , given by the preceding formulæ . Curvature and tortu- osity . curvature ( compare 10. The integral curvature , or whole change of direction of Integral an arc of a plane curve , is the angle ...
... direction cosines of the osculating plane , given by the preceding formulæ . Curvature and tortu- osity . curvature ( compare 10. The integral curvature , or whole change of direction of Integral an arc of a plane curve , is the angle ...
Page 15
... direction is the sum of the composi components ( in that direction ) of the three rectangular com- velocities ... cosines of the inclination of its direction to the given directions are the ratios of the com- ponents to the ...
... direction is the sum of the composi components ( in that direction ) of the three rectangular com- velocities ... cosines of the inclination of its direction to the given directions are the ratios of the com- ponents to the ...
Contents
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| 340 | |
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| 498 | |
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Common terms and phrases
acceleration action algebraic altered angular velocity anticlastic application axis Cambridge centre of inertia circle co-ordinates coefficients component condition configuration constant corresponding course curvature curve cycloidal cylinder denote determined differential equation direction cosines displacement distance dt dt dx dy dy dy dy dz ellipsoid elongation equal equations of motion equilibrium expression finite fixed force formula function geometrical given gyrostatic harmonic motions Hence impulse infinitely small instant integral kinetic energy length linear momentum moving negative osculating plane P₁ parallel particle perpendicular polygon position principal axes quadratic quadratic function quantity radius ratio rectangular resultant right angles rigid body rolling roots rotation round shear simple harmonic simple harmonic motions solution spherical harmonic spherical surface St John's College strain suppose tangent plane theorem tion values whole Y₁ λ² аф
Popular passages
Page 241 - Every body continues in its state of rest or of uniform motion in a straight line, except in so far as it may be compelled by impressed forces to change that state.